Example 7 a sampled group of 50 persons was

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Example - 7 A sampled group of 50 persons was vaccinated to prevent against malaria. Also a control group of 50 persons was observed in the same colony. Following results were obtained. Suffered from Malaria Not Suffered from Malaria Total Vaccinated Not Vaccinated 12 35 38 15 50 50 Total 47 53 100 Can it be concluded that vaccination checks malaria. Here we test, 0 H : Vaccination has nothing to do with the prevalence of malaria Against 1 H : Vaccination prevents the occurrence of malaria. The value of chi-square by the formula is, 2 2 2 2 100(12 15 35 38) 50 50 47 53 100 1150 1150 50 50 47 53 21.23 Tabulated value of 2 for 1 d.f. and =0.05 level of significance is 3.841 which is less than the calculated value of 2 = 21.23. Hence, we reject 0 H . It leads to the conclusion that vaccination prevents malaria. Example - 8 In a survey of 200 children of which 80 were intelligent, 40 has skilled fathers, while 85 of the unintelligent children had unskilled fathers. Do these information support the hypothesis that skilled fathers have intelligent children. Firstly, we tabulated the data in a contingency table of order 2 2 as given below. Fathers Children Skilled Unskilled Total Intelligent Unintelligent 40 40 35 85 75 125 Total 80 120 200 The hypothesis,
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144 0 H : Intelligence of children is independent of skill of fathers. Against 1 H : Skilled fathers have intelligent children can be tested by test. The value of statistic, 2 2 2 2 200(40 85 40 35) 80 120 75 125 200 40 40 50 50 80 120 75 125 8.9 Calculated 2 =8.9 is grater than the tabulated value of chi-square for 1 d.f. and = 0.5 i.e., 3.841. hence, we reject 0 H . It means that skilled fathers have intelligent children. Coefficient of contingency Rejection of the independence of two factors reveals that the factors are associated with each other. But it fails to delineate the strength of dependence. This can be very well measured by coefficient of contingency. The formula for coefficient of contingency is, 2 2 C n Where 2 is the calculated value of statistic chi-square and n sample size. If the value of chi-square is zero, c=0. If 2 is large and n small, the value of c is near zero but never attains 1. If value of c is near zero, it shows a poor degree of dependence. Again a value of chi-square nearing unity shows a high degree of dependency between the two factors. For a contingency table of order 5 5 , the maximum value of c is 0.894. It should be kept in mind that if 2 test shows independence, coefficient if contingency should not be calculated. Example - 9 We calculate the value of coefficient of contingency Suppose a survey is conducted to know the opinion of the workers of a factory whether various types of incentives has got any relationship with category of worker or not. The data collected through the survey are displayed in the table below: Incentive Schemes Category of workers Type-I Type-II Type-III Total Labours Scribes Technical Executive 125(85) 160(138) 65(99) 110(138) 40(34) 65(55.5) 50(40) 30(55.5)
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